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On some convexity questions of Handelman

Part of: Harmonic analysis in several variables Real functions

Published online by Cambridge University Press:  16 May 2024

Brian Simanek Open the ORCID record for Brian Simanek [Opens in a new window]
Brian Simanek*
Affiliation:
Department of Mathematics, Baylor University, Waco, TX 76706, United States
*
e-mail: [email protected]
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Abstract

We resolve some questions posed by Handelman in 1996 concerning log convex $L^1$ functions. In particular, we give a negative answer to a question he posed concerning the integrability of $h^2(x)/h(2x)$ when h is $L^1$ and log convex and $h(n)^{1/n}\rightarrow 1$.

Keywords

Log convex functionsConvexityIntegrable functions

MSC classification

Primary: 26A51: Convexity, generalizations
Secondary: 42B25: Maximal functions, Littlewood-Paley theory
Type
Article
Information
Canadian Mathematical Bulletin , Volume 67 , Issue 4 , December 2024 , pp. 936 - 939
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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References

Handelman, D., Eventual positivity for analytic functions . Math. Ann. 304(1996), no. 2, 315–338.CrossRefGoogle Scholar
Simon, B., Convexity: An analytic viewpoint, Cambridge Tracts in Mathematics, 187, Cambridge University Press, Cambridge, 2011.CrossRefGoogle Scholar